Migration minister Morgan Johansson led the criticism, telling news agency TT that the stunt was “totally ridiculous” and that Sweden Democrats chief Åkesson had only gone to the border to “pose for cameras”.
Åkesson's party confirmed he had visited Greece, writing on Twitter: “We can all remember the migration chaos of 2015 and we have to do everything we can to make sure it never ever happens again.”
Thousands of people have gathered at the Greek frontier since Turkey announced last week that they would not longer be prevented from crossing into the European Union.
Åkesson reportedly handed out flyers with the message “Sweden is full”.
“So if you want to go to Sweden, then that is a bad idea. We don't have the capacity to help more,” Åkesson told newspaper Svenska Dagbladet, adding that he had travelled to the border city of Erdine.
However, other party leaders were quick to criticise the move.
Anders Jonsson, acting Centre Party leader, told TT it was “not worthy of a Swedish party leader” and Jonas Sjöstedt of the socialist Left Party called it “pitiful” in a tweet.
Since entering parliament in 2010, the Sweden Democrats have capitalised on anti-immigrant sentiment, as Sweden has taken in around 440,000 asylum seekers since 2012 (although the number has dropped, with 21,958 people seeking asylum last year).
The party has steadily advanced in the polls. In the most recent 2018 general election, the party won 17.5 percent of the votes, but was not part of government talks with other parties.
An opinion poll published by public broadcaster Sveriges Radio last week suggested the Sweden Democrats were the country's largest party, with over 23 percent support.
This is not the first time the party tries to put refugees off coming to Sweden. Five years ago it was ridiculed by Swedes on Twitter for planning to put adverts in foreign media warning of the Swedish winter.
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